比特币白皮书
Bitcoin:APeer-to-PeerElectronicCashSystem
SatoshiNakamoto
satoshin@gmx.com
www.bitcoin.org
Abstract
Bitcoin:APeer-to-PeerElectronicCashSystem
SatoshiNakamoto
satoshin@gmx.com
www.bitcoin.org
1.Introduction
CommerceontheInternethascometorelyalmostexclusivelyonfinancialinstitutionsservingastrustedthirdpartiestoprocesselectronicpayments.Whilethesystemworkswellenoughformosttransactions,itstillsuffersfromtheinherentweaknessesofthetrustbasedmodel.Completelynon-reversibletransactionsarenotreallypossible,sincefinancialinstitutionscannotavoidmediatingdisputes.Thecostofmediationincreasestransactioncosts,limitingtheminimumpracticaltransactionsizeandcuttingoffthepossibilityforsmallcasualtransactions,andthereisabroadercostinthelossofabilitytomakenon-reversiblepaymentsfornonreversibleservices.Withthepossibilityofreversal,theneedfortrustspreads.Merchantsmustbewaryoftheircustomers,hasslingthemformoreinformationthantheywouldotherwiseneed.Acertainpercentageoffraudisacceptedasunavoidable.Thesecostsandpaymentuncertaintiescanbeavoidedinpersonbyusingphysicalcurrency,butnomechanismexiststomakepaymentsoveracommunicationschannelwithoutatrustedparty.
Whatisneededisanelectronicpaymentsystembasedoncryptographicproofinsteadoftrust,allowinganytwowillingpartiestotransactdirectlywitheachotherwithouttheneedforatrustedthirdparty.Transactionsthatarecomputationallyimpracticaltoreversewouldprotectsellersfromfraud,androutineescrowmechanismscouldeasilybeimplementedtoprotectbuyers.Inthispaper,weproposeasolutiontothedouble-spendingproblemusingapeer-to-peerdistributedtimestampservertogeneratecomputationalproofofthechronologicalorderoftransactions.ThesystemissecureaslongashonestnodescollectivelycontrolmoreCPUpowerthananycooperatinggroupofattackernodes.
2.Transactions
Wedefineanelectroniccoinasachainofdigitalsignatures.Eachownertransfersthecointothenextbydigitallysigningahashoftheprevioustransactionandthepublickeyofthenextownerandaddingthesetotheendofthecoin.Apayeecanverifythesignaturestoverifythechainofownership.
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Theproblemofcourseisthepayeecan'tverifythatoneoftheownersdidnotdouble-spendthecoin.Acommonsolutionistointroduceatrustedcentralauthority,ormint,thatcheckseverytransactionfordoublespending.Aftereachtransaction,thecoinmustbereturnedtotheminttoissueanewcoin,andonlycoinsissueddirectlyfromthemintaretrustednottobedouble-spent.Theproblemwiththissolutionisthatthefateoftheentiremoneysystemdependsonthecompanyrunningthemint,witheverytransactionhavingtogothroughthem,justlikeabank.
Weneedawayforthepayeetoknowthatthepreviousownersdidnotsignanyearliertransactions.Forourpurposes,theearliesttransactionistheonethatcounts,sowedon'tcareaboutlaterattemptstodouble-spend.Theonlywaytoconfirmtheabsenceofatransactionistobeawareofalltransactions.Inthemintbasedmodel,themintwasawareofalltransactionsanddecidedwhicharrivedfirst.Toaccomplishthiswithoutatrustedparty,transactionsmustbepubliclyannounced,andweneedasystemforparticipantstoagreeonasinglehistoryoftheorderinwhichtheywerereceived.Thepayeeneedsproofthatatthetimeofeachtransaction,themajorityofnodesagreeditwasthefirstreceived.
3.TimestampServer
Thesolutionweproposebeginswithatimestampserver.Atimestampserverworksbytakingahashofablockofitemstobetimestampedandwidelypublishingthehash,suchasinanewspaperorUsenetpost.Thetimestampprovesthatthedatamusthaveexistedatthetime,obviously,inordertogetintothehash.Eachtimestampincludestheprevioustimestampinitshash,formingachain,witheachadditionaltimestampreinforcingtheonesbeforeit.
4.Proof-of-Work
Toimplementadistributedtimestampserveronapeer-to-peerbasis,wewillneedtouseaproofof-worksystemsimilartoAdamBack'sHashcash,ratherthannewspaperorUsenetposts.Theproof-of-workinvolvesscanningforavaluethatwhenhashed,suchaswithSHA-256,thehashbeginswithanumberofzerobits.Theaverageworkrequiredisexponentialinthenumberofzerobitsrequiredandcanbeverifiedbyexecutingasinglehash.
Forourtimestampnetwork,weimplementtheproof-of-workbyincrementinganonceintheblockuntilavalueisfoundthatgivestheblock'shashtherequiredzerobits.OncetheCPUefforthasbeenexpendedtomakeitsatisfytheproof-of-work,theblockcannotbechangedwithoutredoingthework.Aslaterblocksarechainedafterit,theworktochangetheblockwouldincluderedoingalltheblocksafterit.
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Theproof-of-workalsosolvestheproblemofdeterminingrepresentationinmajoritydecisionmaking.Ifthemajoritywerebasedonone-IP-address-one-vote,itcouldbesubvertedbyanyoneabletoallocatemanyIPs.Proof-of-workisessentiallyone-CPU-one-vote.Themajoritydecisionisrepresentedbythelongestchain,whichhasthegreatestproofof-workeffortinvestedinit.IfamajorityofCPUpoweriscontrolledbyhonestnodes,thehonestchainwillgrowthefastestandoutpaceanycompetingchains.Tomodifyapastblock,anattackerwouldhavetoredotheproof-ofworkoftheblockandallblocksafteritandthencatchupwithandsurpasstheworkofthehonestnodes.Wewillshowlaterthattheprobabilityofaslowerattackercatchingupdiminishesexponentiallyassubsequentblocksareadded.
Tocompensateforincreasinghardwarespeedandvaryinginterestinrunningnodesovertime,theproof-of-workdifficultyisdeterminedbyamovingaveragetargetinganaveragenumberofblocksperhour.Ifthey'regeneratedtoofast,thedifficultyincreases.
5.Network
Thestepstorunthenetworkareasfollows:
1)Newtransactionsarebroadcasttoallnodes.
2)Eachnodecollectsnewtransactionsintoablock.
3)Eachnodeworksonfindingadifficultproof-of-workforitsblock.
4)Whenanodefindsaproof-of-work,itbroadcaststheblocktoallnodes.
5)Nodesaccepttheblockonlyifalltransactionsinitarevalidandnotalreadyspent.
6)Nodesexpresstheiracceptanceoftheblockbyworkingoncreatingthenextblockinthechain,usingthehashoftheacceptedblockastheprevioushash.
Nodesalwaysconsiderthelongestchaintobethecorrectoneandwillkeepworkingonextendingit.Iftwonodesbroadcastdifferentversionsofthenextblocksimultaneously,somenodesmayreceiveoneortheotherfirst.Inthatcase,theyworkonthefirstonetheyreceived,butsavetheotherbranchincaseitbecomeslonger.Thetiewillbebrokenwhenthenextproofof-workisfoundandonebranchbecomeslonger;thenodesthatwereworkingontheotherbranchwillthenswitchtothelongerone.
Newtransactionbroadcastsdonotnecessarilyneedtoreachallnodes.Aslongastheyreachmanynodes,theywillgetintoablockbeforelong.Blockbroadcastsarealsotolerantofdroppedmessages.Ifanodedoesnotreceiveablock,itwillrequestitwhenitreceivesthenextblockandrealizesitmissedone.
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6.Incentive
Byconvention,thefirsttransactioninablockisaspecialtransactionthatstartsanewcoinownedbythecreatoroftheblock.Thisaddsanincentivefornodestosupportthenetwork,andprovidesawaytoinitiallydistributecoinsintocirculation,sincethereisnocentralauthoritytoissuethem.Thesteadyadditionofaconstantofamountofnewcoinsisanalogoustogoldminersexpendingresourcestoaddgoldtocirculation.Inourcase,itisCPUtimeandelectricitythatisexpended.
Theincentivecanalsobefundedwithtransactionfees.Iftheoutputvalueofatransactionislessthanitsinputvalue,thedifferenceisatransactionfeethatisaddedtotheincentivevalueoftheblockcontainingthetransaction.Onceapredeterminednumberofcoinshaveenteredcirculation,theincentivecantransitionentirelytotransactionfeesandbecompletelyinflationfree.
Theincentivemayhelpencouragenodestostayhonest.IfagreedyattackerisabletoassemblemoreCPUpowerthanallthehonestnodes,hewouldhavetochoosebetweenusingittodefraudpeoplebystealingbackhispayments,orusingittogeneratenewcoins.Heoughttofinditmoreprofitabletoplaybytherules,suchrulesthatfavourhimwithmorenewcoinsthaneveryoneelsecombined,thantounderminethesystemandthevalidityofhisownwealth.
7.ReclaimingDiskSpace
Oncethelatesttransactioninacoinisburiedunderenoughblocks,thespenttransactionsbeforeitcanbediscardedtosavediskspace.Tofacilitatethiswithoutbreakingtheblock'shash,transactionsarehashedinaMerkleTree,withonlytherootincludedintheblock'shash.Oldblockscanthenbecompactedbystubbingoffbranchesofthetree.Theinteriorhashesdonotneedtobestored.
Ablockheaderwithnotransactionswouldbeabout80bytes.Ifwesupposeblocksaregeneratedevery10minutes,80bytes*6*24*365=4.2MBperyear.Withcomputersystemstypicallysellingwith2GBofRAMasof2008,andMoore'sLawpredictingcurrentgrowthof1.2GBperyear,storageshouldnotbeaproblemeveniftheblockheadersmustbekeptinmemory.
8.SimplifiedPaymentVerification
Itispossibletoverifypaymentswithoutrunningafullnetworknode.Auseronlyneedstokeepacopyoftheblockheadersofthelongestproof-of-workchain,whichhecangetbyqueryingnetworknodesuntilhe'sconvincedhehasthelongestchain,andobtaintheMerklebranchlinkingthetransactiontotheblockit'stimestampedin.Hecan'tcheckthetransactionforhimself,butbylinkingittoaplaceinthechain,hecanseethatanetworknodehasacceptedit,andblocksaddedafteritfurtherconfirmthenetworkhasacceptedit.
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Assuch,theverificationisreliableaslongashonestnodescontrolthenetwork,butismorevulnerableifthenetworkisoverpoweredbyanattacker.Whilenetworknodescanverifytransactionsforthemselves,thesimplifiedmethodcanbefooledbyanattacker'sfabricatedtransactionsforaslongastheattackercancontinuetooverpowerthenetwork.Onestrategytoprotectagainstthiswouldbetoacceptalertsfromnetworknodeswhentheydetectaninvalidblock,promptingtheuser'ssoftwaretodownloadthefullblockandalertedtransactionstoconfirmtheinconsistency.Businessesthatreceivefrequentpaymentswillprobablystillwanttoruntheirownnodesformoreindependentsecurityandquickerverification.
9.CombiningandSplittingValue
Althoughitwouldbepossibletohandlecoinsindividually,itwouldbeunwieldytomakeaseparatetransactionforeverycentinatransfer.Toallowvaluetobesplitandcombined,transactionscontainmultipleinputsandoutputs.Normallytherewillbeeitherasingleinputfromalargerprevioustransactionormultipleinputscombiningsmalleramounts,andatmosttwooutputs:oneforthepayment,andonereturningthechange,ifany,backtothesender.
Itshouldbenotedthatfan-out,whereatransactiondependsonseveraltransactions,andthosetransactionsdependonmanymore,isnotaproblemhere.Thereisnevertheneedtoextractacompletestandalonecopyofatransaction'shistory.
10.Privacy
Thetraditionalbankingmodelachievesalevelofprivacybylimitingaccesstoinformationtothepartiesinvolvedandthetrustedthirdparty.Thenecessitytoannouncealltransactionspubliclyprecludesthismethod,butprivacycanstillbemaintainedbybreakingtheflowofinformationinanotherplace:bykeepingpublickeysanonymous.Thepubliccanseethatsomeoneissendinganamounttosomeoneelse,butwithoutinformationlinkingthetransactiontoanyone.Thisissimilartothelevelofinformationreleasedbystockexchanges,wherethetimeandsizeofindividualtrades,the"tape",ismadepublic,butwithouttellingwhothepartieswere.
Asanadditionalfirewall,anewkeypairshouldbeusedforeachtransactiontokeepthemfrombeinglinkedtoacommonowner.Somelinkingisstillunavoidablewithmulti-inputtransactions,whichnecessarilyrevealthattheirinputswereownedbythesameowner.Theriskisthatiftheownerofakeyisrevealed,linkingcouldrevealothertransactionsthatbelongedtothesameowner.
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11.Calculations
Weconsiderthescenarioofanattackertryingtogenerateanalternatechainfasterthanthehonestchain.Evenifthisisaccomplished,itdoesnotthrowthesystemopentoarbitrarychanges,suchascreatingvalueoutofthinairortakingmoneythatneverbelongedtotheattacker.Nodesarenotgoingtoacceptaninvalidtransactionaspayment,andhonestnodeswillneveracceptablockcontainingthem.Anattackercanonlytrytochangeoneofhisowntransactionstotakebackmoneyherecentlyspent.
TheracebetweenthehonestchainandanattackerchaincanbecharacterizedasaBinomialRandomWalk.Thesuccesseventisthehonestchainbeingextendedbyoneblock,increasingitsleadby+1,andthefailureeventistheattacker'schainbeingextendedbyoneblock,reducingthegapby-1.
TheprobabilityofanattackercatchingupfromagivendeficitisanalogoustoaGambler'sRuinproblem.Supposeagamblerwithunlimitedcreditstartsatadeficitandplayspotentiallyaninfinitenumberoftrialstotrytoreachbreakeven.Wecancalculatetheprobabilityheeverreachesbreakeven,orthatanattackerevercatchesupwiththehonestchain,asfollows:
Givenourassumptionthatp>q,theprobabilitydropsexponentiallyasthenumberofblockstheattackerhastocatchupwithincreases.Withtheoddsagainsthim,ifhedoesn'tmakealuckylungeforwardearlyon,hischancesbecomevanishinglysmallashefallsfurtherbehind.
Wenowconsiderhowlongtherecipientofanewtransactionneedstowaitbeforebeingsufficientlycertainthesendercan'tchangethetransaction.Weassumethesenderisanattackerwhowantstomaketherecipientbelievehepaidhimforawhile,thenswitchittopaybacktohimselfaftersometimehaspassed.Thereceiverwillbealertedwhenthathappens,butthesenderhopesitwillbetoolate.
Thereceivergeneratesanewkeypairandgivesthepublickeytothesendershortlybeforesigning.Thispreventsthesenderfrompreparingachainofblocksaheadoftimebyworkingonitcontinuouslyuntilheisluckyenoughtogetfarenoughahead,thenexecutingthetransactionatthatmoment.Oncethetransactionissent,thedishonestsenderstartsworkinginsecretonaparallelchaincontaininganalternateversionofhistransaction.
Therecipientwaitsuntilthetransactionhasbeenaddedtoablockandzblockshavebeenlinkedafterit.Hedoesn'tknowtheexactamountofprogresstheattackerhasmade,butassumingthehonestblockstooktheaverageexpectedtimeperblock,theattacker'spotentialprogresswillbeaPoissondistributionwithexpectedvalue:
Togettheprobabilitytheattackercouldstillcatchupnow,wemultiplythePoissondensityforeachamountofprogresshecouldhavemadebytheprobabilityhecouldcatchupfromthatpoint:
Rearrangingtoavoidsummingtheinfinitetailofthedistribution...
ConvertingtoCcode...
#includedoubleAttackerSuccessProbability(doubleq,intz)
{
doublep=1.0-q;
doublelambda=z*(q/p);
doublesum=1.0;
inti,k;
for(k=0;k<=z;k++)
{
doublepoisson=exp(-lambda);
for(i=1;i<=k;i++)
poisson*=lambda/i;
sum-=poisson*(1-pow(q/p,z-k));
}
returnsum;
}
Runningsomeresults,wecanseetheprobabilitydropoffexponentiallywithz.
q=0.1
z=0P=1.0000000
z=1P=0.2045873
z=2P=0.0509779
z=3P=0.0131722
z=4P=0.0034552
z=5P=0.0009137
z=6P=0.0002428
z=7P=0.0000647
z=8P=0.0000173
z=9P=0.0000046
z=10P=0.0000012
q=0.3
z=0P=1.0000000
z=5P=0.1773523
z=10P=0.0416605
z=15P=0.0101008
z=20P=0.0024804
z=25P=0.0006132
z=30P=0.0001522
z=35P=0.0000379
z=40P=0.0000095
z=45P=0.0000024
z=50P=0.0000006
SolvingforPlessthan0.1%...
P<0.001
q=0.10z=5
q=0.15z=8
q=0.20z=11
q=0.25z=15
q=0.30z=24
q=0.35z=41
q=0.40z=89
q=0.45z=340
12.Conclusion
Wehaveproposedasystemforelectronictransactionswithoutrelyingontrust.Westartedwiththeusualframeworkofcoinsmadefromdigitalsignatures,whichprovidesstrongcontrolofownership,butisincompletewithoutawaytopreventdouble-spending.Tosolvethis,weproposedapeer-to-peernetworkusingproof-of-worktorecordapublichistoryoftransactionsthatquicklybecomescomputationallyimpracticalforanattackertochangeifhonestnodescontrolamajorityofCPUpower.Thenetworkisrobustinitsunstructuredsimplicity.Nodesworkallatoncewithlittlecoordination.Theydonotneedtobeidentified,sincemessagesarenotroutedtoanyparticularplaceandonlyneedtobedeliveredonabesteffortbasis.Nodescanleaveandrejointhenetworkatwill,acceptingtheproof-ofworkchainasproofofwhathappenedwhiletheyweregone.TheyvotewiththeirCPUpower,expressingtheiracceptanceofvalidblocksbyworkingonextendingthemandrejectinginvalidblocksbyrefusingtoworkonthem.Anyneededrulesandincentivescanbeenforcedwiththisconsensusmechanism.
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